A lithographic apparatus is a machine that applies a desired pattern onto a substrate, usually onto a target portion of the substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In that instance, a patterning device, which is alternatively referred to as a mask or a reticle, may be used to generate a circuit pattern to be formed on an individual layer of the IC. This pattern can be transferred onto a target portion (e.g., including part of, one, or several dies) on a substrate (e.g., a silicon wafer).
In lithographic processes, it is desirable frequently to make measurements of the structures created, e.g., for process control and verification. Various tools for making such measurements are known, including scanning electron microscopes (SEM), which are often used to measure critical dimension (CD). Other specialized tools are used to measure parameters related to asymmetry. One of these parameters is overlay, the accuracy of alignment of two layers in a device. Recently, various forms of scatterometers have been developed for use in the lithographic field. These devices direct a beam of radiation onto a target and measure one or more properties of the scattered radiation—e.g., intensity at a single angle of reflection as a function of wavelength; intensity at one or more wavelengths as a function of reflected angle; or polarization as a function of reflected angle—to obtain a “spectrum” of one form or another. The term “spectrum” in this context will be used with a wide scope. It may refer to a spectrum of different wavelengths (colors), it may refer to a spectrum of different directions (diffraction angles), different polarizations, or a combination of any or all of these. From this spectrum a property of interest of the target can be determined. Determination of the property of interest may be performed by various techniques. One particular approach is to perform reconstruction of the target structure by iterative calculations. A mathematical model of the target is created and calculations are performed to simulate interaction of radiation with the target. Parameters of the model are adjusted and calculations repeated until the simulated spectrum becomes the same as the observed spectrum. The adjusted parameter values then serve as a measurement of the real target structure. Each updated model represents a point in “parameter space”, which is a mathematical space with as many dimensions as there are parameters in the model. The aim of the iterative process is to converge to a point in parameter space that represents, at least approximately, the parameters of the actual target structure.
Compared with SEM techniques, optical scatterometers can be used with much higher throughput, on a large proportion or even all of the product units. The optical measurements can be performed very quickly. On the other hand, reconstruction requires a great deal of computation. New processes and target designs can create problems in that known iterative calculations may take a long time to converge on a solution, or may fail to converge.
In some reconstruction techniques, the mathematical model of the target structure is divided into slices, and propagation of radiation is simulated slice-by-slice to arrive at a predicted spectrum. Sloping features are approximated by a staircase in this sliced model. Known reconstruction methods use adaptive slicing as parameters vary. The aim of this is to ensure that the best approximation to the true shape is used at each iteration, without unduly increasing the processing and storage burden. The inventors have recognized that some problems arising when reconstructing some modern designs have a root cause related to this adaptive process.
Calculation methods for simulating interaction of radiation with different structures include for example rigorous coupled wave analysis or RCWA. RCWA is well-known and suitable for application to periodic structures. Other methods such as the differential method and the volume integral method are also known. These other methods are described, for example in the following patent applications: US 2011/218789 A1, WO 2011/48008 A1 and US 2013/066597 A1. The techniques disclosed herein are in no way limited in application to these types of calculations.